Problem: Solve for $x$ and $y$ using elimination. ${3x-2y = -2}$ ${-x-5y = -22}$
We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Multiply the bottom equation by $3$ ${3x-2y = -2}$ $-3x-15y = -66$ Add the top and bottom equations together. $-17y = -68$ $\dfrac{-17y}{{-17}} = \dfrac{-68}{{-17}}$ ${y = 4}$ Now that you know ${y = 4}$ , plug it back into $\thinspace {3x-2y = -2}\thinspace$ to find $x$ ${3x - 2}{(4)}{= -2}$ $3x-8 = -2$ $3x-8{+8} = -2{+8}$ $3x = 6$ $\dfrac{3x}{{3}} = \dfrac{6}{{3}}$ ${x = 2}$ You can also plug ${y = 4}$ into $\thinspace {-x-5y = -22}\thinspace$ and get the same answer for $x$ : ${-x - 5}{(4)}{= -22}$ ${x = 2}$